Question

For each of the following situations involving annuities, solve for the unknown. Assume that interest is compounded annually and that all annuity amounts are received at the end of each period.-interest rate, and n number of years EV of $1, PV of $1, EVA of $1 PVA of $1, EVAD of $1 and PVAD of $ Use appropriate factor(s) from the tables provided. Round your final answers to nearest whole dollar.
Present Value Annuity Amount i = n =
1. ___________ $2,600 8% 5
2. 507,866 135,000 ___ 4
3. 661,241 170,000 9% ____
4. 540,000 78,557 ___ 8
5. 230,000 _____________ 10% 4

Answer 1

Answer:

Following are the solution to the given question:

Explanation:

For point 1:

$Annuity\ Amount= \ 2,600\\\\i=8\%\\\\n=5\\\\Present\ Value=?$

Our table shows that the factor is equal at 3.99271 for 8 percent and 5 periods. In addition to this, the present value is $10,381 dollars in the annuity.

For point 2:

$Present \ Value=507,866\\\\ Annuity \ Amount= 135,000\\\\ i =?\\\\n =4$

$\text{Present Value of Ordinary Annuity = Annuity Amount} \times PVOA \ Factor$

$507,866 = 135,000 \times PVOA \ Factor\\\\\frac{507,866}{135,000} = PVOA \ Factor\\\\3.76197 = PVOA\ Factor$

When looking at our n=4 row table, we notice that perhaps the factor of PVOA is equal to 3,56197 whenever the rate is equal to 2,5%.

For point 3:

$Present\ Value=661,241\\\\ Annuity\ Amount= 170,000\\\\ i = 9\% \\\\n =?$

$\text{Present Value of Ordinary Annuity = Annuity Amount} \times PVOA \ Factor$

$661,241 = 170,000 \times PVOA\ Factor \\\\\frac{661,241}{170,000} = PVOA \ Factor\\\\3.88965 = PVOA \ Factor$

If you really are looking at our table in column i = 9%, we found PVOA is 3.88965 if n is 5.

For point 4:

$Present\ Value= 540,000 \\\\Annuity \ Amount=78,557\\\\ i = ?\\\\n =8$

$\text{Present Value of Ordinary Annuity = Annuity Amount} \times PVOA \ Factor$

$540,000 = 78,557 \times PVOA\ Factor\\\\\frac{540,000}{78,557} = PVOA \ Factor\\\\6.873989 = PVOA \ Factor$

If you verify our table for n = 8 lines, the PVOA factor is approximately 6.87399 when the rate of interest is 3.5 percent.

For point 5:

$Present\ Value=230,000\\\\ Annuity\ Amount=?\\\\ i =10\%\\\\ n =4$

The PVOA factor is 3.16997 when we search our table with i = 10% and n = 4.

$230,000 = Annuity \ Amount \times 3.16987\\\\\frac{230,000}{3.16987} = Annuity\ Amount\\\\72,558 = Annuity\ Amount\\\\annuity\ total= \ 72,558.$